First-Year Mathematics for Secondary Schools

Cover First-Year Mathematics for Secondary Schools
First-Year Mathematics for Secondary Schools
Breslich, Ernst R. (Ernst Rudolph), 1874-
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201, be two right triangles having the hypotenuse (side opposite the right angle) AC equal to AiCi and EC ^ Bid.
Place AAiBiCi adjacent to AABCf making BiCi coincide with the equal side BCy so that A and Ai he on opposite sides of BC.
Then ABAi is a straight hne and the figure ACAi a triangle.
Why?
Show that AACAi is an isosceles triangle.
Why?
(a.s.a.) Why?
Fig. 201 Hence Prove Then ZA = ZAi.
AABC^AAiBC: AAiBiCi^AABC.
EXERCISES Prove the following: 1. Two right triangles are congruent if the t
...wo sides about the right angle of one are respectively equal to the two sides about the right angle of the other.
Digitized by Google ' CONGRUENCE OF TRIANGLES 161 2. Two right triangles are congruent if the hypotenuse and an acute angle of one are respectively equal to the hypotenuse and an acute angle of the other.
3. Theorem: The shortest distance from a point to a line is the perpendiciUar from the point to the line.
For, let ABy Fig. 202, be perpendicular to DE A and let AC be any other Une from A to DE.


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